Percentage and profit loss new version 4

METHODS

Eight Techniques1

APPLICATIONS

In Commerce, Geometry etc.,

2

LINKS

Profit & Loss & other links

3

PERCENTAGE

SIX PHRASE – VEERARAGAVAN C.Shttp://182.72.85.213:8080/AssessmentTool http://www.facebook.com/SixPhrase

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PRESENTER NAME SIX PHRASE – The Finishing School 1 I

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SESSION CONTENT

• In this session, we shall learn application of percentage concept in problems in the areas of geometry & commerce including profit / loss.

• Percentage concepts used in other areas such as alligations / mixtures are dealt under the respective session topics.

02-03-2015VEERARAGAVAN C S, APTITUDE TRAINER,

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X% of a Number

An x % increase

An x% decrease

40% OF 20 MEANS 40

100𝑋20 = 8.

1) If 20% of a = b, then b% of 20 is the same as:

A.4% of a B. 5% of a C.20% of a D. None of these

20% of a = b 20

100𝑋𝑎 = 𝑏

b% of 20 = 𝑏

100𝑋20

b% of 20 = 20

100𝑋𝑎𝑋

1

100𝑋20 =

4𝑎

100

X% of a Number

An x % increase

An x% decrease

Increase by 40% means 140% of that number.

III.The price of a product becomes `54 after it increases by 35%. What was the original price of that product? 1)30 2)36 3)40 4)45

Increase by 35% means 135% of the price is 54. 135

100𝑋 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 = 54 Hence the original price is 54 𝑋

100

135= 40.

X% of a Number

An x % increase

An x% decrease

Decrease by 40% means (100–40)60% of that number.

V. The price of a product is reduced to Rs.72 after it is decreased by 10%. What is the original price of the product? 1)84 2)90 3)96 4)80

Decreased by 10% means 90% of that price.

Hence the original price is 72 𝑋100

90= 80.

90

100𝑋𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 = 72

Calculating a percent changeBasically, a percent is a simple

𝑝𝑎𝑟𝑡

𝑤ℎ𝑜𝑙𝑒ratio

times 100. When they ask you tocalculate percent changes, and here youhave to be very careful with order, i.e.,what’s the starting number and what’sthe ending number.

IMPORTANT: in a percent change, thestarting number is always 100%. Thus,we can say:

Percent change = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒

𝑆𝑡𝑎𝑟𝑡𝑖𝑛𝑔 𝑁𝑢𝑚𝑏𝑒𝑟𝑋100

Here are a couple examples

a) Price increases from `400 to `500; findthe percentage increase.

Of course, that’s a change of `100, so`100 divided by starting value of `400 is

0.25, times 100 is 25%. A move from `400 to ` 500 is a 25% increase.

• b) Price decreases from ` 500 to ` 400;find the percentage decrease.

• Change is still ` 100, but now the

starting value is ` 500, and `100

500=

0.20, times 100 is 20%. A move from` 500 to ` 400 is a 20% decrease.

• BIG IDEA: Order matters. When youchange from one value to anotherand want the percentage change, itmatters which value was the startingvalue.


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PERCENT CHANGE

The population of a town increased from 1,75,000 to 2,62,500 ina decade. The average percent increase of population per yearis: A.4.37% B.5% C.6% D.8.75%

Increase in 10 years = (262500 - 175000) = 87500.

Here the starting number is 175000.

Increase% =87500

175000𝑋100% = 50%.

Required average =50

10%= 5%.


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Percentage

increased by x % then decreased by y % then resulting effect in percent

+x – y –𝑥𝑦

100

Increased by x% then again increased by y% then

+x+y+𝑥𝑦

100

Decreased by x% then increased by y%

–x+y –𝑥𝑦

100

Decreased by x% then again decreased by y%

– x – y + 𝑥𝑦

100


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If the value of something is

I.If the price of a shirt is increased by 10% than decreased by 10%. What is the percent change?

+ 10 - 10 –10 10

100= - 1%

The best way to speed up calculations is to eliminate the need of calculations.

9.Rajeev buys good worth Rs. 6650. He gets arebate of 6% on it. After getting the rebate, hepays sales tax @ 10%. Find the amount he willhave to pay for the goods.

A. Rs. 6876.10 B. Rs. 6999.20

C. Rs. 6654 D. Rs. 7000

Total percentage = −6 + 10 −60

100= +3.4%

Amount he will pay = 6650 ∗103.4

100= 6876.10


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PERCENTAGE OF PROFIT & LOSS100 oranges are bought at the rate of Rs. 350 and

sold at the rate of Rs. 48 per dozen.

The percentage of profit or loss is:

A. 1427

% gain B.15% gain C. 1427

% loss D.15 % loss

C.P of 100 oranges = Rs.350

S.P of 100 oranges =4812

x100 = 400.

Profit % =400 −350

350𝑥100 = 14

27

% gain


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Profit percentage

If the cost price of x articles isequal to the selling price of yarticles, then the profit percentage

is given by: 𝑥 − 𝑦100

𝑦

If Sudha sells 18 articles at the cost price of 24 articles. Find her profit percentage?

Here, x= 24 and y= 18

24 − 18100

18=

100

3= 33

1

3%

02-03-2015 11

Usual MethodLet C.P of 1 article be Rs.xThen C.P of 24 articles = 24xS.P of 18 articles = 24x

S.P of 1 article = 24𝑥

18

Profit % =

24𝑥

18−𝑥

𝑥𝑋100

= 24𝑥 − 18𝑥100

18

=100

3= 33

1

3%

QUANTITYThe cost price of 20 articles is the same as theselling price of x articles.

If the profit is 25%, then the value of x is:

A. 15 B. 16 C. 18 D. 25

Profit% =x−2020

𝑥100= 25.

X – 20 = 5

X = 25.


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TOTAL GAIN / LOSSA shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%.

His total gain or loss percent is:

A. 51517

% loss B. 51517

% gain C. 623

% gain D. None of these

C.P. of 1st transistor = 100120

𝑥840 = Rs.700

C.P. of 2nd transistor = 10096

x 960 = Rs.1000

So, total C.P. = Rs. (700 + 1000) = Rs. 1700.

Total S.P. = Rs. (840 + 960) = Rs. 1800.

Gain % =1800 −1700

1700x 100 = 5

1517

% gain.


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PROFIT IN MIXTUREA trader mixes 26 kg of rice at Rs. 20 per kg with 30 kgof rice of other variety at Rs. 36 per kg and sells themixture at Rs. 30 per kg.

His profit percent is:

A. No profit, no loss B. 5%

C. 8% D. 10% E. None of these

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36)

= Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain =1680−1600

1600𝑥100 = 5%


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SELLING PRICE

A man buys a cycle for Rs. 1400 and sells it at a loss of 15%.

What is the selling price of the cycle?

A. Rs. 1090 B. Rs. 1160

C. Rs. 1190 D. Rs. 1202

S.P = 85100

𝑋1400= Rs.1190


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SELLING PRICE

The percentage profit earned by selling an article for Rs. 1920 isequal to the percentage loss incurred by selling the same articlefor Rs. 1280.

At what price should the article be sold to make 25% profit?

A. Rs. 2000 B. Rs. 2200

C. Rs. 2400 D. Data inadequate

SP1 – CP = CP – SP2 means CP =SP1+SP2

2=

1920+12802

=1600.

New SP =125100

x 1600 = Rs.2000.


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Selling Price

By selling a horse for Rs570 a trader loses 5%. Atwhat price must he sell it togain 5%.

Selling Price(SP)

= given(Rs) X 100±𝑄

100±𝑔𝑖𝑣𝑒𝑛%

Selling Price

= 570 X 100+5

100−5=Rs.630


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USUAL METHODS.P = 570 and loss 5%

C.P = 100

100−𝑙𝑜𝑠𝑠𝑥𝑆. 𝑃

=100

95𝑥570

Profit = 5%So new S.P

=100+𝑃𝑅𝑂𝐹𝐼𝑇

100𝑋𝐶. 𝑃

= 105

100𝑥

100

95𝑋570

=Rs.630

SELLING PRICEWhen a plot is sold for Rs. 18,700, theowner loses 15%.

At what price must that plot be sold inorder to gain 15%?

A. Rs. 21,000 B.Rs. 22,500

C. Rs. 25,300 D.Rs. 25,800

S.P = Given Amt x100 ± 𝑄𝑢𝑒𝑠𝑡𝑖𝑜𝑛

100 ±𝑔𝑖𝑣𝑒𝑛 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒

= 18700 x11585

= Rs.25,300


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Given S.P = 18,700Loss = 15%

C.P = 100

100 −lossx S.P

= 10085

X18700

Required = Profit 15%

S.P=100+𝑝𝑟𝑜𝑓𝑖𝑡

100𝑋𝐶. 𝑃

=115100

𝑋10085

𝑋18700

SELLING PRICEA vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?

A. 3 B. 4 C. 5 D. 6

C.P of 6 toffees = `.1

S.P of 6 toffees = 120100

𝑋1 =120100

For `120100

, no of toffees sold = 6.

For `1, no of toffees sold = 100120

x 6 = 5.


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COST PRICEOn selling 17 balls at Rs. 720, there is a loss equal to

the cost price of 5 balls.

The cost price of a ball is:

A. Rs. 45 B. Rs. 50

C. Rs. 55 D. Rs. 60

(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)

C.P. of 12 balls = S.P. of 17 balls = Rs.720.

C.P of 1 ball = 72012

= Rs.60


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PERCENTAGE ERROR

2.A student multiplied a number by3

5instead of

5

3. What is the

percentage error in the calculation?

A.34% B.44% C.54% D.64%

Error = correct value – wrong value =5

3−

3

5=

16

15

Percentage error =𝐸𝑟𝑟𝑜𝑟

𝐶𝑜𝑟𝑟𝑒𝑐𝑡𝑋100 =

16

155

3

𝑋100=16

15𝑋

3

5𝑋100

64%


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PERCENTAGE IN SETS

3.In a certain school, 20% of students are below 8 yearsof age. The number of students above 8 years of age isof the number of students of 8 years of age which is 48.What is the total number of students in the school?A.72 B.80 C.120 D.150 E.100

Number of students of 8 years of age = 48.

Number of students of 8 years above = 48.

80% of students = 96.

Hence No. of students = 96 𝑋100

80=120.


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PERCENTAGE IN SETS

5.In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was: A.2700 B.2900 C.3000 D.3100

Number of valid votes = 80% of 7500 = 6000.

Valid votes polled by other candidate = 45% of 6000=2700.


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PERCENTAGE IN SETS

6.Three candidates contested an election and received1136, 7636 and 11628 votes respectively.

What percentage of the total votes did the winningcandidate get?

A. 57% B. 60% C. 65% D. 90%

Total number of votes polled = (1136 + 7636 + 11628) = 20400.

Required perecentage = 1162820400

𝑋100% = 57%


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PERCENTAGE IN RATIO

4. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B. A.2 : 3 B. 1 : 1 C. 3 : 4 D. 4 : 3


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5% of A + 4% of B =2

(6% of A + 8% of B)3

5A +

4B =

2(

6A +

8B)

100 100 3 100 100

1A +

1B =

1A +

4B

20 25 25 75

1-

1A =

4-

1B

20 25 75 25

1A =

1B

100 75

5% of A + 4% of B = 2

3 6% 𝑜𝑓 𝐴 +

5% of A + 4% of B = 4% of A + 16

3% of B

1% of A =16

3− 4 % of B

1% of A = 43% of B

A=

100=

4.

B 75 3 Required ratio = 4 : 3

PERCENTAGE IN ALGEBRA

7.Two tailors X and Y are paid a total of Rs. 550 per week by theiremployer. If X is paid 120 percent of the sum paid to Y, howmuch is Y paid per week?

A.Rs. 200 B. Rs. 250 C.Rs. 300 D.None of these

Let the sum paid to Y per week be Rs. z.

Then, z + 120% of z = 550.

𝑧 +120

100𝑧 = 550.

220

100𝑧 = 550.

Z = 550X100

220=250.


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8.Gauri went to the stationers and bought things worth Rs. 25,out of which 30 paise went on sales tax on taxable purchases. Ifthe tax rate was 6%, then what was the cost of the tax freeitems?

A. Rs. 15 B. Rs. 15.70 C. Rs. 19.70 D. Rs. 20

6% of taxable = 30

100.

Cost of taxable = 30

100𝑋

100

6=5.

Cost of tax free items = 25 – 5 = Rs.20.


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12.Two students appeared at an examination. One of themsecured 9 marks more than the other and his marks was 56% ofthe sum of their marks. The marks obtained by them are:

A. 39, 30 B.41, 32 C. 42, 33 D.43, 34

One student secured 44% of the sum of marks.

Second student secured 56% of the sum of marks.

Difference = 12% of the sum of marks = 9 marks.

Sum of marks = 10012

𝑋9=75.

Hence first scored 44100

𝑋75=33 and second scored = 42.


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PERCENTAGE IN RACES & GAMES

11.A batsman scored 110 runs which included 3boundaries and 8 sixes. What percent of his total scoredid he make by running between the wickets?

A. 45% B.455

11% C.54

6

11% D.55%

Total runs not by running = 3x4 + 8x6 = 12+48=60.

Percent of his total score he made by running = 60

110𝑋100 = 54

6

11%


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13.A fruit seller had some apples. He sells 40% applesand still has 420 apples. Originally, he had:

A. 588 apples B. 600 apples

C. 672 apples D. 700 apples

60% of apples = 420.

Originally he had = 100

60𝑋420

=700 apples.


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PERCENTAGE IN NUMBER SYSTEM

14.What percentage of numbers from 1 to 70 have 1 or 9 in theunit's digit? A.1 B.14 C.20 D.21

numbers from 1 to 70 that have 1 or 9 in the unit's digit are

1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

Required percentage = 14

70X100

=20%


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PERCENTAGE IN NUMBER SYSTEM15.If A = x% of y and B = y% of x, then which of the following is true?

A. A is smaller than B. B. Relationship between A and B cannot be determined.

C. A is greater than B D. If x is smaller than y, then A is greater than B.

E. None of these

A = x% of y


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= 𝑥

100𝑋𝑦 =

𝑥𝑦

100=

𝑦𝑥

100

=𝑦

100𝑋𝑥 = y% of x

= B.

PROFIT & LOSS

C.S.VEERARAGAVAN


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Profit & Loss

There are two shopkeepers having shopsside by side.The first shopkeeper sells bicycles.He sells a bicycle worth $30 for $45.One day a customer comes and buys abicycle.He gives a $50 note to the shopkeeper.The shopkeeper doesn't have change so hegoes to the second shopkeeper, gets thechange for $50, and gives $5 and thebicycle to the customer.The customer goes away.The next day the second shopkeeper comesand tells the first shopkeeper that the $50note is counterfeit and takes his $50 back.Now, how much does the first shopkeeperlose?


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From the second shopkeeper he took$50 and gave back $50 so there was noprofit no loss. To the customer he gave$5 + $30 bicycle. Therefore, his totalloss is $35

PROFIT / LOSSIf a man purchase 11 orange forRs 10 and sell them 10 for Rs11. How much profit or loss didhe made?

Profit or loss made = 11𝑋11−10𝑋10

10𝑋10X100 =21% profit.

If 'a' articles are bought for Rs'b' and sell them 'c' for Rs 'd'.Then profit or loss made by thevendor:

𝑎𝑑 − 𝑏𝑐

𝑏𝑐𝑥100


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USUAL METHODC.P of 11 oranges Rs.10

C.P of 1 orange is Rs.10

11.

S.P of 10 oranges Rs.11

S.P of 1 orange is Rs.11

10

Profit or loss made

= 𝑆.𝑃 −𝐶.𝑃

𝐶.𝑃𝑋 100

=11

10−

10

1110

11

𝑋 100

= 11𝑋11 −10𝑋10

110𝑋

11

10𝑋100

= 11𝑋11−10𝑋10

10𝑋10𝑋100

Example 2

A boy buys orange 9 forRs. 16 and sell them 11for Rs. 20. Find profit orloss percentage.

profit or loss percent made : 9𝑋20−11𝑋16

11𝑋16𝑥100 =

25

11% 𝑝𝑟𝑜𝑓𝑖𝑡


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Did the original problem really have so much information in it ? Yeeeeesssssss ---only if you go down deep enough.It is IMPOSSIBLE to get to solutions like these, if you tend to rush through to the solution using the most familiar ways known to you.

PROFIT PERCENTAGE

Some articles were bought at 6 articles for Rs. 5and sold at 5 articles for Rs. 6. Gain percent is:

A. 30% B. 3313

% C. 35% D. 44%

Gain % =36−2525

𝑥100 = 44%


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PROFIT PERCENTAGE

A shopkeeper expects a gain of 22.5% on his cost price.

If in a week, his sale was of Rs. 392, what was hisprofit?

A. Rs. 18.20 B. Rs. 70

C. Rs. 72 D. Rs. 88.25

C.P =100122.5

x392 = Rs.320.

Profit = Rs.392 – Rs.320 = Rs.72.


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PROFIT PERCENTAGE

Sam purchased 20 dozens of toys at the rate of Rs. 375 perdozen.

He sold each one of them at the rate of Rs. 33.

What was his percentage profit?

A.3.5 B.4.5 C.5.6 D.6.5

C.P of 1 toy =37512

= 31.25

S.P = 33.

Profit % =33 −31.2531.25

x100

=1.7531.25

x100 = 5.6%


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C.P = Rs.375 per dozenS.P = 33 x 12 = Rs.396

Profit % = 396 −375

375x100

= 21375

x 100

= 285

PROFIT PERCENTAGE

Alfred buys an old scooter for Rs. 4700 and spends Rs.800 on its repairs.

If he sells the scooter for Rs. 5800, his gain percent is:

A. 447

% B. 5511

% C.10% D. 12%

Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.

Selling Price (S.P.) = Rs. 5800.

Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.

Gain% =3005500

𝑋100 = 5511

%


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PROFIT PERCENTAGEIf selling price is doubled, the profit triples.

Find the profit percent.

A.6623

B. 100 C. 10513

D. 120

Let C.P be x . S.P = y. Profit = y – x .

Given 3(y – x) = 2y – x.

Y = 2x.

Profit % =y−xx

𝑋 100=xx𝑋100= 100.


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PROFIT PERCENTAGE

In a certain store, the profit is 320% of the cost. If thecost increases by 25% but the selling price remainsconstant, approximately what percentage of the sellingprice is the profit?

A.30% B. 70% C.100% D. 250%

Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.

New C.P. = 125% of Rs. 100 = Rs. 125

New S.P. = Rs. 420.

Profit = Rs. (420 - 125) = Rs. 295.

Profit % =295420

x100 =5984

x100 ≈6084

x100 =5007

= 70%.


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Date post:	16-Jul-2015
Category:	Education
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Percentage and profit loss new version 4

Education